# How to Sell High-Dimensional Data Optimally

arXiv: https://arxiv.org/abs/2510.15214 · HTML: https://mlsanity.com/paper/2510.15214/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 56 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Algorithmic Bayesian Persuasion](https://mlsanity.com/paper/1503.05988/) (2015)
- [Duality and Optimality of Auctions for Uniform Distributions](https://mlsanity.com/paper/1404.2329/) (2014)
- [Understanding Incentives: Mechanism Design becomes Algorithm Design](https://mlsanity.com/paper/1305.4002/) (2013)
- [Exact Semidefinite Formulations for a Class of (Random and Non-Random) Nonconvex Quadratic Programs](https://mlsanity.com/paper/1802.02688/) (2018)
- [On the tightness of SDP relaxations of QCQPs](https://mlsanity.com/paper/1911.09195/) (2019)
- [The Economics of Social Data](https://mlsanity.com/paper/2004.03107/) (2020)
- [How to Sell Information Optimally: an Algorithmic Study](https://mlsanity.com/paper/2011.14570/) (2020)
- [Optimal Pricing of Information](https://mlsanity.com/paper/2102.13289/) (2021)
- [Multi-dimensional Virtual Values and Second-degree Price Discrimination](https://mlsanity.com/paper/1404.1341/) (2014)
- [Optimal Mechanism Design for Single-Minded Agents](https://mlsanity.com/paper/2002.06329/) (2020)

## Built on by (most cited first, 1 of 1)

- [Learning to Price with Persuasion](https://mlsanity.com/paper/2608.16699/) (2026)

## Abstract (arXiv)

Motivated by the problem of selling large, proprietary data, we consider an information pricing problem proposed by Bergemann et al. that involves a decision-making buyer and a monopolistic seller. The seller has access to the underlying state of the world that determines the utility of the various actions the buyer may take. Since the buyer gains greater utility through better decisions resulting from more accurate assessments of the state, the seller can therefore promise the buyer supplemental information at a price. To contend with the fact that the seller may not be perfectly informed about the buyer's private preferences (or utility), we frame the problem of designing a data product as one where the seller designs a revenue-maximizing menu of statistical experiments. Prior work by Cai et al. showed that an optimal menu can be found in time polynomial in the state space, whereas we observe that the state space is naturally exponential in the dimension of the data. We propose an algorithm which, given only sampling access to the state space, provably generates a near-optimal menu with a number of samples independent of the state space. We then analyze a special case of high-dimensional Gaussian data, showing that (a) it suffices to consider scalar Gaussian experiments, (b) the optimal menu of such experiments can be found efficiently via a semidefinite program, and (c) full surplus extraction occurs if and only if a natural separation condition holds on the set of potential preferences of the buyer.